Before we can think about where hate comes, we need to define "hate". As I said before, there are certain groups in society who label anything and anyone they don't agree with as "hate" or "hateful".
For example, I personally believe that burning the American flag is hateful and an act of terrorism. The person who burns the American flag might view their act as an expression of dissatisfaction, or oppression, or maybe they just woke up that day and felt like it. That person might feel that even though I am offended by it, it doesn't necessarily represent hate, and it's their right as a citizen to do so.
Who is right? Who decides whose viewpoint is correct? This is where it gets complicated.
The OP's article associating the word "incel" and "terrorist" is over the top and reckless. Although their viewpoints can be considered vulgar and offensive, it is an irresponsible leap to label them "terrorists" just because they say things you don't like.
Public censure is one thing. Hysteria and witch hunts are another thing altogether. Are "incels" the new "satanic cults" of the 80's and early 90's?
Actually, it wasn't the OP's opinion, it was the state of Texas that has made the designation. I'm going to go ahead and assume that's because they know more about it than we see in the news.
I don't consider promoting and committing violence against women (and others) to be simply vulgar and offensive. And Incels have been tied to many crimes, including mass murders, as noted in the article I posted upthread.